QUANTUM COMPUTING - EXAMPLE 32.2 : (a) If | 001 > = | 1 >, | 111 > = | 7 >, find the 2 possible values of ( | 001 > + | 1 > + | 7 > ) ( | 111 > ). (b) In quantum money, a duplicate will have probability P of passing the verification test of a bank, if the total number of photons on the bank note is N. The would be counterfeiter has a probability p of success in duplicating the quantum money correctly for each photon. Guess the relationship of P, p and N as a mathematical formula involving natural logarithm ln.
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QUANTUM COMPUTING - ANSWER 32.2 : (a) First answer : ( | 001 > + | 1 > + | 7 > ) ( | 111 > ) = ( | 1 > + | 1 > + | 7 > ) ( | 111 > ) = ( | 9 > ) ( | 111 > ) = | 999 >. Second answer : ( | 001 > + | 1 > + | 7 > ) ( | 111 > ) = ( | 1 > + | 1 > + | 7 > ) ( | 7 > ) = ( | 9 > ) ( | 7 > ) = | 63 >. (b) If N = 1, then P = p. If N = 2, then P = p power 2. If N = 3, then P = p power 3. For N, P = p power N, ln P = ln (p power N), then ln P = N ln p. The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
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